Question

1. if given the side lengths of a triangle, show or explain how you could determine if it is a right triangle.

Explanation:

Step1: Identify the longest side

Let the side lengths be $a$, $b$, $c$, where $c$ is the largest.

Step2: Apply Pythagorean theorem

Check if $a^2 + b^2 = c^2$.

Step3: Verify equality

If the equation holds, it is a right triangle.

Answer:

1. First, identify the longest side of the triangle (label it $c$, and label the other two sides $a$ and $b$).
2. Calculate the sum of the squares of the two shorter sides: $a^2 + b^2$.
3. Calculate the square of the longest side: $c^2$.
4. If $a^2 + b^2 = c^2$, the triangle is a right triangle; if not, it is not a right triangle. This is based on the converse of the Pythagorean theorem.